Question

Question 8: (12 marks) For this question you are required to find the standard deviation for a set of data. The answer alone will not achieve full marks. There are many tools available to calculate the standard deviation. Here you are required to use several of the tools and show your working out to earn the marks. The data is the test results of 21 students who sat a mathematics quiz worth 100 marks. Results: 60, 47, 17, 43, 30, 90, 77, 61, 54, 89, 22, 80, 67, 37, 63, 50, 81, 21, 36, 51, 59. a) Calculate the mean and variance and standard deviation using a scientific calculator. (3 marks) b) Calculate the standard deviation by long hand showing all workings step-by-step. (3 marks) c) Set up a spreadsheet to calculate the standard deviation. Insert a screen shot or snip to show the data and the answer. (3 marks) d) Use an on-line calculator to find the mean, variance and standard deviation of the data. Insert a screen shot or snip to show the three answers.

Answer 1

b Buy hand Solution a By using Scientific calculator mean = 50.04762 Variance = 460.99773 Setendard deviation = 21.47086 b) By hand mean = {x = 135 = 54.84762 variance = {(x-2)2 9680.952 . 60 35-4308 u7 49.689 17 1372.526 u3 122.05 30 578.288 90 1292.574 77 526.8117 u8.3856 0.0023 89 21 su 22 80 122 1.67 1027.05 673.526 1. 21 1460.99773 nance = 21.07086 16707641 37 290.6213 63 50 8) 8o.1451 16-3832 726-u31 1092.lus 21 36 51 325.7166 9-28798 20.526) 59 035 De 9680.952

Mean = 54.04762 variance= 484.0476 std. dev = 22.00108 Count, N: 21 Sum, Ex: 1135 Mean, 54.047619047619 Variance, 02460.9977324263 Steps o= {(oz – w " i=1 (X-X)^2 35.43083 49.66895 1372.526 122.0499 578.288 1292.574 526.8117 48.33559 0.002268 1221.669 1027.05 673.526 167.7641 290.6213 80.14511 16.38323 726.4308 1092.145 36 325.7166 51 9.287988 59 24.52607 Totall 11359680.952 62 - E(X; -M.)2 - (60 - 54.047619047619)2 + ... + (59 - 54.047619047619)2 21 9680.9523809524 21 = 460.9977324263 o = 460.9977324263 = 21.470857747801